POKER FACE: According to team sources, Donnie Walsh is reluctant to deal Anthony Randolph to the Timberwolves for a first-round pick, which could be used in a deal to acquire Carmelo Anthony. Photo: AP

Donnie Walsh (Paul J. Bereswill)

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SALT LAKE CITY — Of the concerns team president Donnie Walsh has in breaking up the Knicks for Carmelo Anthony, one of them is having to use Anthony Randolph in a deal with the Timberwolves for a first-round pick, The Post has learned.

With a new report suggesting Anthony may not sign an extension with the Nets, with that three-team deal on hold and Amar’e Stoudemire texting Anthony to tell him to spurn Jersey, the Knicks have some new life, though they still appear long shots.

The best-case scenario for the 22-16 Knicks, who lost 131-125 to the Jazz last night, is for the Nuggets to get desperate if Anthony officially shuns the Nets and demands a New York trade. The Rockets reportedly will swoop in, too, and could be willing to offer more than Walsh.

The Knicks feel Anthony holds all the cards, and Walsh plans to play the cards he has carefully, not desperately. He is unwilling to give up too much for Anthony, team sources said yesterday.

Walsh is waffling on whether he even wants to part with Randolph to gain a first-round pick from the Timberwolves, a selection he possibly would have to ship with two of three prospects — Danilo Gallinari, rookie sensation Landry Fields or restricted free agent Wilson Chandler.

Walsh will not give up three of those four players, knowing the Knicks’ biggest need is a legit starting center. Sources said restricted free agents Marc Gasol and Clippers 7-footer DeAndre Jordan are squarely on the radar this summer, and that’s a big priority.

For now, the Knicks wait patiently on the periphery, realizing Anthony’s advisors are eager to drag them into the race to give the Nets competition. The Knicks’ chances, sources say, have been helped slightly because the prospects who could be available to Denver have played well.

Having Stoudemire’s support on a Anthony trade is also a factor, league sources believe.

On Monday, the Nuggets reportedly made a threat to Nets management about trading him to the Knicks if leaks on their trade talks don’t stop.

Even by gaining a first-round pick to trade, it still may not be enough to satisfy Denver, which would get two first-rounders from the Nets.

Walsh has hoped Anthony’s desire to play for the Knicks would prompt him to go to free agency this summer when the Knicks have cap room.

With the Knicks winning, developing a great chemistry and having players at Anthony’s position, but not at center, Walsh is more likely to give a modest proposal unsuitable to the Nuggets.

Walsh believes the club has a lot of solid small-forward types such as Anthony but what they need is a “beast” of a center to get them to the next level.

The Knicks have for months been long shots for Anthony because they don’t have two suitable first-round picks to offer in a deal like the Nets do. Nevertheless, the Knicks, according to a league source, have a contingent deal in place with Minnesota to trade Randolph for a Timberwolves 2011 first-round pick. The Knicks have to own a first-round pick this season because they league rules prohibit them from going two straight years without one.

Though the 6-foot-11 Randolph is out of the rotation and seemingly off coach Mike D’Antoni’s radar, Walsh is unsure he wants to give up on him because he is just 21 years old, and size and athleticism is a rare commodity. D’Antoni, however, does not like Randolph’s in-game demeanor and he doesn’t carry a high-enough motor.

D’Antoni has talked about developing 7-foot-1 center Timofey Mozgov for later this season, making a comparison to Toney Douglas’ rookie season. Douglas took over the starting point guard role in the final month when D’Antoni felt he was ready for it.